Reducing Iterations of Grover Search Algorithm for N-Queen Problem U sing Quantum Permutation States

In this paper, we propose a construction method of Grover's algorithm to solve the N-Queen problem. Quantum permutation state was designed and applied to the initialization and amplitude amplification process in Grover's algorithm. An oracle-level quantum circuit was constructed using Boolean algebraic expressions. We reduced the number of iterations of the Grover's algorithm by decreasing the number of superposed inputs in the initialize step using quantum permutation state. We show that our algorithm has less time complexity compared to previous study that solved the N -Queen problem using Grover's algorithm with W state as a input.